Specifics of Creating a Public Transport Demand Model for Low-Density Regions: Lithuanian Case

Abstract

A transport model usually consists of a demand model and an available transport network model. The purpose of this article is to identify the key specifics for the development of a regional public transport (PT) demand model and to point out the differences from the urban PT demand model. The traditional four-step transport planning demand model consists of trip generation, trip distribution, modal split, and assignment. This article consists of PT model development, calibration, and validation. A PTV VISUM macroscopic modeling program is used for this research. As a result, this article presents basic suggestions for how a PT demand model should be developed in regions. The presented suggestions for developing a PT demand model can be applied to any low-density region. The rest of the article is structured as follows: (1) Background: presents a literature analysis of the four-step model, modal splits, and the features of the PTV VISUM program; (2) Methods: describes the considered region of Lithuania and the data of the developed model; describes the four-step model, which is adapted to the Lithuanian region; (3) Results: presents the results and main suggestions for creating a PT demand model; and (4) Conclusions: presents the main conclusions of the study.

1. Introduction

Public transport (PT) is a widely used form of transport around the world. PT is an important indicator that reflects the possibilities of public mobility. In order for the public to prioritize PT, an attractive, easily accessible and developed PT system must be offered in all populated areas, maintaining its integrity. Many foreign countries pay great attention to the planning, improvement and development of PT networks. A well-developed PT infrastructure, networks of passenger connections and mixed territory construction contribute to the growth of regional development and are extremely important for the labor market in regions and the fight against segregation [1].

Running a public transportation system is a crucial undertaking for both urban and rural areas, facilitating the movement of people and goods and serving as a significant contributor to the economic development of these regions [2]. Transport poverty exists in both urban and rural areas, but the consistent absence of options, such as a regular and well-connected bus system, is an ingrained characteristic of rural transport services [3]. Significant hurdles in rural areas include the sparse population density and considerable distances between localities, posing challenges to delivering high-quality public transportation that can match the living conditions found in urban areas [4]. Because rural areas have a low population density, offering public transportation often proves economically inefficient, leading to a dependence on private cars. Traditionally, rural areas have leaned on private transport. This arises from lengthy travel distances, a sparse local population density, and the seasonal nature of temporary residents’ stays in rural areas, making it difficult to establish an effective and sustainable PT service as a viable alternative to private vehicles [5].

Coordinating efficient transportation in rural areas can be challenging, given the vast distances and limited passenger flows. Conventional PT may not be the most cost-effective solution in such scenarios. Shared-use mobility services present a potential solution for rural and sparsely populated areas with restricted access to PT, such as by replacing underutilized PT vehicles [6].

A well-developed PT system and mixed-use urban development are very important in creating an attractive county/region. In order to organize the PT service as conveniently as possible, and to make it passenger-oriented, modeling methods are used. Modeling is a popular and effective operations research technique used to analyze many dynamically changing systems [7].

Transport modeling helps to analyze the level and distribution of traffic flows in a road network and the passenger flows in PT [8]. Two types of models are used in traffic modeling: micro and macroscopic. Both types of models differ in the way they take into account vehicles in the flow and the description of their movement. Microscopic models simulate the characteristics and interactions of individual vehicles. They essentially create the trajectories of vehicles moving through the network. The following microscopic simulation programs are widely used: VISSIM, SUMO, MATSim, TRANSIMS, SATURN, etc. [9,10]. Macroscopic modeling is used to model regional PT. This sort of modeling has the benefit of allowing for the analysis and investigation of a wider flow network. The model must accurately mirror reality to produce outcomes that are realistic [11]. Macroscopic models simulate the total flow of vehicles on a road rather than individual vehicles. Three important variables in macroscopic models are the vehicle flow, speed, and density [10]. The following macroscopic modeling programs are most widely used: CUBE Voyager, TransCAD, VISUM, Strada, Metacor, Emme, Transyt, KRONOS, etc. [10,12].

A transport model usually consists of a demand model and an available transport network model. The demand model requires travel demand data; the network model describes the relevant data of the transport system [13]. The development of the macroscopic model consists of two interrelated stages: creation of transport supply information, which is represented by the network of streets and roads, traffic zones, PT parameters, etc., and transport demand calculations using a classic four-step mathematical model, the initial data of which are information about a population, workplaces, the number of pupils and students, the locations of educational institutions, and the modal distribution [8,14].

Travel demand models play a crucial role in examining hypotheses related to policies, emerging mobility concepts, and regulations. As cities and regions evolve, the use of these models has become increasingly important for creating efficient and sustainable transportation networks that meet the evolving needs of communities and contribute to the development of smart, interconnected urban environments [15]. The demands regarding transport services include a high quality and differentiation. The need for transport is very diverse, differentiated according to different times of day or days of the week, and depends on the destination, the importance of travel speed and service frequency, and more [16].

The proposed approach includes problem definition, model objectives, development, calibration, validation, scenario creation, simulation experiments, and evaluation [17]. This article presents PT model development, calibration, and validation. It is hypothesized that the same specifics of PT demand modeling cannot be applied to cities and regions. The purpose of this article is to identify the key specifics for the development of a regional PT demand model.

2. State of the Art

The primary objective of transportation planning and management is to align the availability of transportation with travel demand. In transportation planning, a decision-making process is employed for future road infrastructure upgrades within a region. Several programming software and manuals have been developed to assist in this decision-making process, and one such tool is travel demand prediction models that are used for implementing a four-step planning process [18]. The traditional four-step model is an example of trip-based transportation modeling [19]. Numerous European cities, particularly those that are small to medium-sized, have persisted in employing the traditional strategic four-step modeling approach for various reasons. These reasons encompass factors such as inadequate data, a shortage of technical expertise, and the preference for simpler models [20]. The widely adopted four-step transportation demand forecasting models are currently utilized in the majority of cities and regions to inform decision-making processes associated with transportation planning [21]. The traditional four-step transport planning demand model consists of:

• Trip generation. This step determines of the number of trips generated and taken depending on the motivation to travel in individual transport zones, taking into account functional characteristics and key statistics, such as population, the number of jobs, the number of school places, retail and service space, etc.
• Trip distribution. This step determines the travel ratio (where trips originate and end), taking into account the potential of transport regions and the distances between them.
• Modal split. In this step, trips are classified by the mode of transport (public, private), creating an origin–destination (OD) matrix for each mode of transport.
• Assignment. At this stage, the trips in the OD matrix are assigned to potential networks or routes [7,22,23,24,25,26].

There is very little in the literature describing demand modeling for low-density areas. This scarcity of the literature in regional contexts underscores the challenges in developing comprehensive demand models for low-density areas. Despite these limitations, this study aims to contribute valuable insights by examining the effectiveness of the selected trip models in capturing the unique dynamics of transportation demand in low-density populated regions. A PT service to such areas is vital as it is sometimes the only mode of transport to complete the journey. Modal split information is typically collected through surveys, transportation studies, and government agencies, and it may vary based on the region, urbanization level, and other factors. The modal split denotes the proportionate distribution of various transportation modes, such as road or rail, within the overall transportation modes. In the case of passengers, the distribution is determined for each mode based on the total passenger kilometers, following the principle of territoriality. The current modal split analysis focuses on inland transport, including passenger cars, buses, coaches, and trains. From 2010 to 2019, passenger cars constituted 82.0% to 83.1% of the European Union’s (EU) inland passenger transport. Due to the COVID-19 pandemic, the car share increased to 87.2% in 2020, while coaches, buses, and trolley buses decreased to 7.4%. In 2021, passenger cars remained dominant at 86.3%, with buses and trolleybuses at 7.7% and trains at 6.0%. After examining EU member states, Montenegro recorded the highest proportion of passenger car usage at 98.5%, followed by Lithuania at 94.7%. Conversely, Turkey and Hungary had the lowest shares, with 74.0% and 79.3%, respectively [27].

A macroscopic modeling program was used in this research. The macroscopic simulation program PTV VISUM 21 was employed to conduct simulations for the case study analysis. PTV VISUM is macroscopic modeling software designed for transportation network planning and analysis [28]. PTV VISUM software was used for planning and to simultaneously assess transportation planning, travel demand modeling, and GIS network data management. PTV VISUM serves as the tool for creating intricate transport network plans and addressing traffic-related issues, combining a thorough data analysis with efficient computation. This software assists public transportation planners in developing methodologies to enhance and optimize existing PT networks [29]. Its user-friendly interface and powerful analytical capabilities make it the preferred choice for professionals working in the transportation and urban planning sectors.

2.1. Trip Generation

The process of developing a demand model begins by determining the amount of passenger traffic generated and absorbed in each zone. Flow production is the part of the generated flow that describes the traffic “out of” the area. Flow attraction is the part of the generated flow that describes the traffic “into” the zone [30].

The trip generation stage determines the number of trips generated in and targeted at traffic areas based on land use and socio-economic data, such as demographic and population data [31]. The population of each transport zone should be divided into different groups to reflect different mobility behavior. A larger number of person groups (children, schoolchildren, students, seniors, working population, unemployed, etc.) allows for a detailed calibration of the model, but also reflects population changes under future scenarios (e.g., demographic effects). The factors for the distribution of the population data by groups of persons can be determined from a pre-existing household mobility survey [32].

Currently, there are two approaches to traffic modeling: trip-based modeling and activity-based modeling [33]. The primary distinction between the two methodologies lies in their focus. The conventional trip-based modeling approach concentrates on individual trip types, such as the journey from home to work. In contrast, activity-based modeling centers around activities that generate trips and utilizes them to create trip sequences or chains, such as home–work–shopping–leisure [34].

In cities, the percentage of PT use is higher. The general characteristics of local travel differ from regional travel (longer distances, often less frequent services, fewer stops, etc.) [35]. The reality is that many rural areas have few running buses and only a few kilometers of cycle and walking paths, and they almost totally depend on cars. Securing equal mobility rights poses a greater challenge in rural or sparsely populated areas.

The production of and motivation for trips in cities are obtained in the following manner:

$$P_i=p_k·BK+p_s·BS$$

(1)

$$A_i=a_k·BK+a_s·BS$$

(2)

where $P_i$—production of zone i, $A_i$—attraction of zone i, $p_k, p_s$—factor of production for residential houses and apartments, $a_k, a_s$—factor of attraction for residential houses and apartments, and $BK, BS$—number of residential houses and apartments [36].

The evaluation of trip generation factors in the city is carried out by distinguishing several zones based only on the characteristics of residential houses (zones with family houses and zones with apartments in buildings where there is no transit transport). After determining the boundaries of such zones, the calculation of the amount of vehicles entering and leaving these zones is carried out. Multiplying the number of vehicles during the morning and afternoon peak periods by the average vehicle occupancy factor and then dividing by the number of houses/apartments gives the estimated pull and production factors [37]. Unlike cities, it would be difficult to conduct such a study in regions. In order to determine the attraction and production of passenger flows in the regions, demographic (population) and statistical data are collected.

2.2. Trip Distribution

The demand for PT is changing over time. A reliable OD matrix is essential for transportation analysis and planning, as it provides spatio-temporal trip estimates that enable planners to understand which modes people use, how long they travel, and where they go [38]. An OD matrix can be categorized as either static or dynamic. A static OD matrix involves flows that are independent of time and distributed across space. Methodologies have been devised for this category to represent average flows between OD pairs within a geographic area, typically in a single matrix. Examples include gravity models, entropy maximization, and information minimization. On the other hand, the focus shifts to dynamic OD matrices in the realm of transportation planning, as they provide a more accurate depiction of traffic dynamics between zones. Initial methods for estimating the OD matrix relied on statistical inference derived from interviews and/or surveys. Nonetheless, advancements in monitoring individual movements within a network have allowed for the modeling of dynamic and more precise matrices depicting the state of urban traffic. This is made feasible through sensory data sources like mobile phone records, global positioning system trajectories, and smart card records [39].

In the realm of public transportation, an OD matrix, detailing the starting and ending points for each passenger (Table 1), holds significant importance for optimizing bus networks. The OD matrix for bus passenger flow aims to identify the initial and final stops for individual passengers. These data serve as the foundation for urban bus network planning and management, offering reliable support for bus operation scheduling and network optimization. The conventional survey method involves distributing forms to passengers upon boarding, in which they are required to fill in their origins and destinations. The collected forms are then gathered when passengers disembark. However, this survey method is labor-intensive and consumes substantial human, material, and financial resources. Furthermore, operational challenges arise, such as the convenience for passengers to complete forms and the level of passenger cooperation, making it difficult to ensure the accuracy of the survey data [40].

Recently, numerous public transportation systems have adopted modern technologies like automated fare collection, vehicle location, and weighing systems to monitor passenger flows. These technologies yield valuable data (smart card details, automatic vehicle weights) for estimating the OD matrix. Nevertheless, obtaining these data can be expensive due to the installation and maintenance of measurement equipment. Widespread implementation may lead to excessive expenses, requiring a careful evaluation of costs in relation to the benefits of a more accurate OD matrix [41].

Table 1. The trips from origin and destination zone [42].

Zone		Destination							Sum
		1	…	…	j	…	…	n	Oi
	1	t1−1	…	…	t1−j	…	…	t1−n	O1
	…	…
	…	…
Origin	i	ti−1	…	…	ti−j	…	…	ti−1	Oi
	…	…
	…	…
	n	tn−1	…	…	tn−j	…	…	tn−n	On
Sum Dj		D1	…	…	Dj	…	…	Dn	T

Table 1. The trips from origin and destination zone [42].

Zone		Destination							Sum
		1	…	…	j	…	…	n	Oi
	1	t1−1	…	…	t1−j	…	…	t1−n	O1
	…	…
	…	…
Origin	i	ti−1	…	…	ti−j	…	…	ti−1	Oi
	…	…
	…	…
	n	tn−1	…	…	tn−j	…	…	tn−n	On
Sum Dj		D1	…	…	Dj	…	…	Dn	T

An economical and straightforward approach is essential for predicting PT demand. Utilizing OD data obtained from on/off data allows for the identification of assignment flows and passenger loads within a transport network. Knowing the number of trips at a specific station enables the determination of the origin of each destination trip. This is accomplished through the application of a gravity model, wherein the distance between regions and the volume of trips to and from stations are employed to estimate the number of trips between these stations [43]. The gravity model approach involves estimating each cell in the OD matrix without relying on existing travel patterns, in contrast to growth factor approaches [19]. The gravity model equation is:

$$T_{ij}=\frac{P_i·A_j·F_{ij}}{\sum _{j=1}^n{A}_j·F_{ij}}$$

(3)

where $T_{ij}$—the number of trips starting in zone i and ending in zone j, $P_i$—the number of trips starting in zone i, $A_j$—the number of trips ending in zone j, and $F_{ij}$—the combined coefficient calculated from the empirically determined combined function [36].

In this model, the number of trips between regions is proportional to the value of the generating potential of the initial zone and the absorption potential of the final zone and inversely proportional to the distance measured in terms of travel time [26].

The spatial distribution of trips is described using the combined function (Equation (4)), which describes the decreasing number of trips as the distance between regions increases [44]. This function describes how the distance of a trip (often measured in travel time) affects the probability of completing it [26].

$$f\left(t_{ij}\right)=a·t_{ij}^b·c^{c·t_{ij}}$$

(4)

where $t_{ij}$—the travel time between zones i and j and $a, b, c$—function parameters [45].

2.3. Modal Split

The demand model defines the number of trips between different zones with different destinations using different transport systems. Only one type of transport system has been used in this study—PT (buses)—covering trips of all types of inhabitants. Thus, the demand model is presented with only one OD matrix and other transport modes were not analyzed.

2.4. Assignment

The final stage of the four-stage model involves the modeling of PT network flow assignments. A route assignment model is required to assign trips between origins and destinations in a traffic demand model based on an OD matrix. Most of the procedures for trip assignment models are empirical and depend on traffic and route conditions. Essentially, trip assignment methods can be broadly categorized into two groups: static trip assignment methods and dynamic trip assignment methods. The static trip assignment method primarily centers on the transportation planning process, estimating the traffic loading on network links. Conversely, the dynamic trip assignment method is employed to model time-varying traffic flows in network links, indicating how congestion levels change over time [19].

Assignment models can be categorized into three primary types: frequency-based, timetable-based, and simulation-based models. Frequency-based models focus on aggregated frequencies along transit lines, aiming to calculate the ridership share percentage for each line. Simulation-based models monitor the real-time route selection of transit users. On the other hand, timetable-based models treat each vehicle trip independently, utilizing a modeling scheme that represents each vehicle’s departure time through a diachronic graph [46].

This paper uses a trip assignment of passenger flows based on a timetable-based assignment method, for which a Logit model for the distribution of passenger flows is defined:

$$U=e^{-\beta ·R}$$

(5)

where $U$—the distribution of passenger flows, $\beta =0.25$—a function parameter, and $R$—the impedance of a connection [47].

A PT traveler chooses the route that causes the least inconvenience. The severity of the trip is measured by taking into account all stages of the trip: accessibility of the stop, waiting for PT, possible interchange at an integrated node or between nodes, waiting for another type of PT, and the destination of the journey from the final stop.

The trip assignment stage determines the value of the impedance indicator (IPD), which shows what most determines the mode and route of travel. The IPD is calculated according to Equation (6).

$$IPD=a·PJT+b·FP$$

(6)

where $IPD$—impedance indicator, $PJT$—perceived journey time, $a, b$—coefficients, and $FP$—fare point [48].

The perceived journey time (PJT) is calculated using Equation (7):

$$PJT={\alpha }_1·IVT+{\alpha }_2·ART+{\alpha }_3·AT+{\alpha }_4·ET+{\alpha }_5·WT+{\alpha }_6·OWT+{\alpha }_7·TWT+{\alpha }_8·NT$$

(7)

where $PJT$—perceived journey time, $IVT$—in-vehicle time (time spent in PT), $ART$—PT Aux ride time (PT journey time), $AT$—access time (walking time to the starting stop), $ET$—egress time (walking time to the destination (from the last drop-off stop)), $WT$—walk time (total walking time on foot), $OWT$—origin wait time (waiting time at the first stop), $TWT$—transfer wait time, and $NT$—number of transfers [48].

2.5. Model Calibration and Validation

To make sure that the model can reflect the current state of flows, it is necessary to check the results. This is achieved by comparing the observed passenger trip data (count value) with the results of the modeling process.

It is important to note that the baseline model must accurately reflect reality. Calibration ensures that the results accurately reflect the observed behavior and data [11]. Calibration is performed to obtain the best possible agreement between the simulated (simulation) and measured (actual) values of passenger volume. Compared to regions, it is easier to collect real data in cities. A unified electronic ticket system contributes significantly to data collection in cities. It is more difficult for passenger carriers in the regions to collect data on passenger flows.

Model development and calibration are part of an iterative process that leads to model validation. This means that the data collected should be structured in the same format as the data generated by the model. Macroscopic validation can help us refine the model [49]. Validation is achieved by measuring the output of the baseline model calibration against the observed data, which is not the same as the data used to calibrate the model; comparing the data; and assessing the accuracy [50]. In addition, validation criteria should be defined, specifying the main hypotheses and the choice of statistical tests to be applied. If there are differences between the model results and the real-world data, the model needs to be corrected and validated again. Validating a traffic simulation model requires a lot of skill and perseverance [17].

There are several methods for comparing real flows with model flows with techniques such as root mean square error (RMSE), percent root mean square error (%RMSE), the coefficient of determination (R²), the mean absolute difference ratio (MAD ratio), and the Geoffrey E. Havers (GEH) indicator [19,51]. The GEH indicator is recommended in urban areas (cities), since it overcomes the problem due to having a high variation in traffic flows [19]. It is employed to establish a connection between the observed and simulated traffic flow. Calibration and validation results demonstrate a robust correlation in traffic flow between the experimental and simulated data, as indicated by the GEH statistic [52]. The GEH statistic is a statistical technique used in traffic engineering, forecasting, and modeling to compare sets of traffic volumes (Equation (8)).

$$GEH=\sqrt{\frac{{(V_s-V_o)}^2}{(V_s+V_o)/2}}$$

(8)

where o—observed data, s—simulated data, and V—volume of simulated (V_S) and field data (V_O) [53].

A model is considered calibrated when 85% of the total traffic volume exhibits a GEH coefficient below 5.0. Conversely, if the GEH coefficient exceeds 10.0, the model is deemed uncalibrated, rendering the collected data and simulation model output irrelevant [54]. The use of the GEH indicator as an acceptability criterion for travel demand forecasting models is recognized in the UK Highways Agency’s Road and Bridge Design Guide, the Wisconsin Microscopic Modelling Guidelines, the Transport for London Traffic Modelling Guidelines, and other references [28].

This study uses the coefficient of determination—a measure of the difference between the modeled and observed values of the dependent variable—to calibrate and validate the model. The higher the value of the determination coefficient, the better the model fits the data.

3. Introduction to Lithuanian Case

Tauragė County, a Lithuanian region, was selected for the model study. Tauragė County consists of four municipalities: Jurbarkas, Pagėgiai, Šilalė, and Tauragė. Tauragė County has a total area of 4408 km², with a population density of 21 inhabitants/km². Tauragė County includes 39 elderships (a branch of the municipal administration [55]) and 3 cities: Tauragė, Jurbarkas, and Šilalė. PT carriers UAB “Tauragės autobusų parkas”, UAB “Jurbarko autobusų parkas”, UAB “Šilalės autobusų parkas”, and UAB “Autokeda” all provide services to the districts of Tauragė County.

The biggest problem for passenger transportation in Lithuania is suburban PT routes. Most routes are not served on all working days or are only served once a day, and some municipalities are served only a few times a week [56]. This research examines one type of PT—buses. Seasonal and weekend routes are not evaluated in this work. There are 14 PT routes in the Šilalė district municipality, 2 PT routes in the Pagėgiai municipality, 18 PT routes in the Jurbarkas district municipality, and 32 PT routes in the Tauragė district municipality. All these PT routes run every weekday. There are 20 intercity PT routes that can be used to travel between municipalities.

According to the newest mobility research presented in the Tauragė Sustainable Mobility Plan [57], 28% of the population travels to work by bus and 15% travels by bus to places of education.

The public institution Green Region (original—“Žaliasis regionas”) was established in Lithuania by four municipalities in the Tauragė region (Jurbarkas, Pagėgiai, Šilalė, and Tauragė). Green Region is responsible for fostering regional economic growth, boosting investment appeal, enhancing tourism-related activities, and coordinating regional PT services. Also, Green Region, in September 2022, initiated six regional bus routes by which residents can travel for free every working day.

The PT road network and PT stops of the four municipalities of Tauragė County were imported with the help of General Transit Feed Specification (GTFS) data. The authors adjusted the GTFS data—the network data were adjusted according to the latest information from the Lithuanian Road Administration, and the data of the PT stops and PT routes schedules were adjusted according to the official information provided by the Green Region. According to the lowest administrative division—the elderships—the boundaries of the zones and their number coincide with the number of municipalities of Tauragė County. A total of 39 zones are defined. In total, the Tauragė County macroscopic model contains 628 nodes, 1374 links, 1112 connectors, 529 stop points, 92 lines, and 247 line routes.

4. Explanation of Modeling

4.1. Trip Generation

In city models, during the trip generation step, special zones are identified for large travel attractors and producers: primary and secondary schools, hospitals and clinics, universities, factories, administrative urban centers, business zones, airports, shopping centers, large recreation centers, parks, etc. In cities, trip models are selected based on their functional nature and basic statistical data, such as population, the number of jobs, the number of seats in schools, medical facilities, the area of retail and service facilities, etc.

When collecting detailed data, a lack of data from the regions is encountered; data are not collected, saved, or divided into larger units. In order to create the Green Region OD matrix, demographic (population) and statistical data were collected, such as the working population (WP), the number of jobs (J), the number of students and school children (SCH), the capacity of educational institutions (inhabitants from 7 to 30 years old) (EI), the number of pre-school children (CH), and the capacity of pre-schools (children up to 7 years old) (PSCH). Demographic and statistical data were collected to determine the output and attraction of passenger flows and are presented in

Table A1. Collected demographic and statistical data.

No	Zone/Elderly	WP	J	SCH	CH	EI	PSCH
1	Batakiai	424	9	71	102	0	0
2	Gaurė	815	236	127	196	0	0
3	Lauksargiai	467	78	70	102	0	0
4	Mažonai	1155	319	178	261	0	0
5	Skaudvilė	1151	385	188	277	644	0
6	Tauragė city	8921	8414	1330	1972	4666	775
7	Tauragė el.	1883	1081	310	503	0	34
8	Žygaičiai	841	82	134	174	201	0
9	Eržvilkas	786	41	109	124	241	0
10	Girdžiai	373	56	60	73	0	0
11	Juodaičiai	145	1	32	22	0	0
12	Jurbarkas city	4069	4000	663	862	1726	228
13	Jurbarkai	1066	914	181	208	0	152
14	Raudonė	394	0	67	67	0	0
15	Seredžius	742	261	114	114	197	0
16	Skirsnemunė	666	93	92	148	227	0
17	Smalininkai	390	360	76	90	370	0
18	Šimkaičiai	575	111	128	119	134	0
19	Veliuona	480	186	85	62	238	0
20	Viešvilė	289	116	62	70	86	0
21	Bijotai	339	15	51	84	0	0
22	Bilioniai	144	41	22	33	0	0
23	Didkiemis	88	2	20	22	0	0
24	Kaltinėnai	813	187	128	135	289	0
25	Kvėdarna	1211	416	218	261	412	131
26	Laukuva	988	162	158	213	360	0
27	Palentinis	87	0	16	27	0	0
28	Pajūris	679	344	140	159	320	0
29	Šilalė city	2095	2418	320	419	1578	312
30	Šilalė kaimiškoji	1114	325	201	236	0	0
31	Teneniai	155	0	38	29	0	0
32	Traksėdis	612	270	129	146	0	0
33	Upyna	606	72	101	132	0	0
34	Žadeikiai	271	0	51	64	0	0
35	Lumpėnai	371	5	61	75	0	0
36	Natkiškiai	264	37	52	61	61	0
37	Pagėgiai	1343	709	208	278	456	155
38	Stoniškiai	625	78	98	131	62	0
39	Vilkyškiai	508	568	81	116	222	0

that is included in Appendix A.

This work examines six trip models (Figure 1):

• Home–work (H-W) (production is defined by the WP; attraction is defined by J);
• Work–home (W-H) (production is defined by J; attraction is defined by the WP);
• Home–educational institution (H-E) (production is defined by SCH; attraction is defined by EI);
• Educational institution–home (E-H) (production is defined by EI; attraction is defined by SCH);
• Home–pre-school (H-S) (production is defined by CH; attraction is defined by PSCH);
• Pre-school–home (S-H) (production is defined by PSCH; attraction is defined by CH).

The production and attraction results generated by PTV VISUM 21 software for each trip model are shown in

Table A2. The production and attraction results.

No	Zone/Elderly	P/H-W	A/H-W	P/W-H	A/W-H	P/H-E	A/H-E	P/E-H	A/E-H	P/H-S	A/H-S	P/S-H	A/S-H
1	Batakiai	0	9	9	424	0	0	0	71	0	0	0	102
2	Gaurė	0	236	236	815	0	0	0	127	0	0	0	196
3	Lauksargiai	0	78	78	467	0	0	0	70	0	0	0	102
4	Mažonai	0	319	319	1155	0	0	0	178	0	0	0	261
5	Skaudvilė	0	385	385	1151	0	644	0	188	0	0	0	277
6	Tauragė city	775	8414	8414	8921	775	4666	775	1330	775	775	775	1972
7	Tauragė el.	34	1081	1081	1883	34	0	34	310	34	34	34	503
8	Žygaičiai	0	82	82	841	0	201	0	134	0	0	0	174
9	Eržvilkas	0	41	41	786	0	241	0	109	0	0	0	124
10	Girdžiai	0	56	56	373	0	0	0	60	0	0	0	73
11	Juodaičiai	0	1	1	145	0	0	0	32	0	0	0	22
12	Jurbarkas city	228	4000	4000	4069	228	1726	228	663	228	228	228	862
13	Jurbarkai	152	914	914	1066	152	0	152	181	152	152	152	208
14	Raudonė	0	0	0	394	0	0	0	67	0	0	0	67
15	Seredžius	0	261	261	742	0	197	0	114	0	0	0	114
16	Skirsnemunė	0	93	93	666	0	227	0	92	0	0	0	148
17	Smalininkai	0	360	360	390	0	370	0	76	0	0	0	90
18	Šimkaičiai	0	111	111	575	0	134	0	128	0	0	0	119
19	Veliuona	0	186	186	480	0	238	0	85	0	0	0	62
20	Viešvilė	0	116	116	289	0	86	0	62	0	0	0	70
21	Bijotai	0	15	15	339	0	0	0	51	0	0	0	84
22	Bilioniai	0	41	41	144	0	0	0	22	0	0	0	33
23	Didkiemis	0	2	2	88	0	0	0	20	0	0	0	22
24	Kaltinėnai	0	187	187	813	0	289	0	128	0	0	0	135
25	Kvėdarna	131	416	416	1211	131	412	131	218	131	131	131	261
26	Laukuva	0	162	162	988	0	360	0	158	0	0	0	213
27	Palentinis	0	0	0	87	0	0	0	16	0	0	0	27
28	Pajūris	0	344	344	679	0	320	0	140	0	0	0	159
29	Šilalė city	312	2418	2418	2095	312	1578	312	320	312	312	312	419
30	Šilalė kaimiškoji	0	325	325	1114	0	0	0	201	0	0	0	236
31	Teneniai	0	0	0	155	0	0	0	38	0	0	0	29
32	Traksėdis	0	270	270	612	0	0	0	129	0	0	0	146
33	Upyna	0	72	72	606	0	0	0	101	0	0	0	132
34	Žadeikiai	0	0	0	271	0	0	0	51	0	0	0	64
35	Lumpėnai	0	5	5	371	0	0	0	61	0	0	0	75
36	Natkiškiai	0	37	37	264	0	61	0	52	0	0	0	61
37	Pagėgiai	155	709	709	1343	155	456	155	208	155	155	155	278
38	Stoniškiai	0	78	78	625	0	62	0	98	0	0	0	131
39	Vilkyškiai	0	568	568	508	0	222	0	81	0	0	0	116

that is included in Appendix A.

4.2. Trip Distribution

An OD matrix provides valuable information to improve the service quality of public transportation systems [58]. An OD matrix represents the count of passengers journeying between every pair of origin and destination points [43].

In order to determine the gravity model of the OD matrix, a combined function is created. The combined function (Equation (4)) is calculated using the parameters a, b, and c, which were selected based on studies carried out for regions with a similar area (4409 km²) and population density (20.8 inhabitants per km²). The function parameters (

Table 2. The parameters of trip models with a combined function.

Trip Models	a	b	c
H-W, W-H	0.242	1.166	−0.388
H-E, E-H	0.245	1.579	−0.5
H-S, S-H	0.245	1.579	−0.5

) for the study were selected from the most similar region—Aglomeracja Rybnicka (Poland)—whose area is 224 km² and population density is 349 inhabitants per km² [59].

Figure 2 shows what the combined function looks like for H-E, E-H, H-S, S-H trip models, and Figure 3 shows what the combined function looks like for H-W and W-H trip models.

Travel demand is aggregated at the zonal level and presented in the form of an OD matrix. The OD matrix defines how many trips originate in zone Z_i and travel to zone Z_j [13]. Comparing a region’s OD matrix with a city’s OD matrix, a region’s OD matrix has many fields with a value of 0. This means that there are no travelers from zone Z_i to Z_j and vice versa. This is not the case in a city’s OD matrix, since there is a higher demand for PT in cities. It is also easier to estimate passenger transfers in city models.

4.3. PT Assignment

The case study areas where chosen the public institution Green Region operates consist of four regional districts: Tauragė, Pagėgiai, Šilalė, and Jurbarkas. Green Region conducted a survey at the beginning of 2022 to determine the PT needs of Tauragė region’s residents. There was a total of 661 respondents from the municipalities of Tauragė County. A total of 9% of respondents were from the Pagėgiai municipality, 30% were from the Šilalė district municipality, 39% were from the Tauragė district municipality, and 22% were from the Jurbarkas district municipality. Survey respondents were asked to rate their satisfaction with the PT infrastructure and timetables. Of those surveyed, 46% were dissatisfied, 37% were somewhat satisfied, and only 17% were satisfied.

According to the survey, 28% of people do not use PT because they have their own car, 27% find the PT schedules inconvenient, 21% cannot use it because it does not go to their destination, and 14% are unable to travel by PT from their place of residence. Most respondents (58%) would be encouraged to use PT if there was a greater variety of routes, and 28% would be encouraged by cheap or free PT.

The biggest causes of dissatisfaction with PT were identified as:

• Some districts do not have access to cities;
• Inconvenient timetables;
• Lack of PT routes;
• Inadequate density of bus stops.

Meanwhile, city residents were more often dissatisfied with the low frequency of PT services, bus overcrowding, long travel times, and bus delays, which are influenced by traffic congestion in cities, since cities are characterized by a smaller territorial area with a higher density of vehicles. Taking into account the results of a regression analysis study performed by the authors [60], the number of passengers on suburban routes is mostly influenced by the bus mileage, the unemployment rate, and the number of buses, while the number of passengers on intercity routes depends on the number of bus routes and the bus mileage. People who do not work in the municipalities of the region make fewer trips, so their dependence on the PT system is not as high as those who work.

Taking into account the results of the regression analysis performed by the authors [60] and the results of the population survey carried out by Green Region, the formulas for the IPD (Equation (9)) and PJT (Equation (10)) are as follows:

$$IPD=1·PJT+0·FP$$

(9)

$$PJT=2·IVT+2·ART+4·AT+4·ET+1·WT+3·OWT+2·TWT+20·NT$$

(10)

In cities, the peak hours model is usually used, as the highest passenger flows are reached during the morning peak hours, when the most important problems become apparent. This is not suitable for region models. In areas with a lower demand, it would not be possible to develop a model only during peak hours, as it would not have the required level of reliability due to low passenger flows. Therefore, when modeling PT in regions, one should choose either a period of one working day or a period of working weeks. Taking into account the fact that in some municipalities of Tauragė County, there are routes that run only on certain days of the working week (not every day) with limited hours, even just once a day, the research period of demand was chosen as five working days (from Monday to Friday) from 0:00 to 24:00. Based on the collected data on PT passenger flows, the model was run from 1 September 2022 to 30 September 2022.

5. Presentation of Findings of the Research

5.1. Model Calibration and Validation

In this study, the coefficient of determination (R-squared statistic) was calculated. The calibration compares actual PT passenger flow data (X) with model data (Y).

The output shows the results (

Table 3. Double-squared dependency.

Parameter	Least Squares Estimate	Standard Error	T Statistic	p-Value
Intercept	−6.14467 × 106	3.35938 × 106	−1.82911	0.0707
Slope	3.89124	0.160779	24.2024	0.0000

and

Table 4. Analysis of variance.

Source	Sum of Squares	Df	Mean Square	F-Ratio	p-Value
Model	5.79267 × 1017	1	5.79267 × 1017	585.76	0.0000
Residual	8.90028 × 1016	90	9.8892 × 1014
Lack-of-Fit	8.85307 × 1016	69	1.28305 × 1015	57.08	0.0000
Pure Error	4.72037 × 1014	21	2.2478 × 1013
Total (Corr.)	6.6827 × 1017	91

) of fitting a double-squared model to describe the relationship between Y and X.

Because the p-value in the ANOVA table is less than 0.05, there is a statistically significant relationship between the model attribute and the observed attribute at the 95.0% confidence level.

The equation of the fitted model is:

$$Y=\sqrt{(-6.14467\times {10}^6+3.89124·X^2)}$$

(11)

The R-squared statistic indicates that the model as fitted explains 86.6816% of the variability in Y (Figure 4). The result shows that the model’s passenger flows are highly consistent with the actual values. The correlation coefficient is 0.93103, indicating a relatively strong relationship between the variables.

The standard error of the estimate, indicating a standard deviation of residuals, is 3.14471 × 10⁷. The mean absolute error, with an average residual value, is 1.00849 × 10⁷. The Durbin–Watson statistic assesses the residuals for any significant correlation based on their sequential order in the data file.

The coefficient of determination (R-squared statistic) is greater than 85%. Based on the simulation results from both calibration and validation, it can be concluded that the baseline model has been constructed accurately. This indicates that the model is a true reflection of the existing system and can be utilized for any modifications to the transportation network.

5.2. Main PT Demand Model Results

In cities, the distance to the nearest PT stop is much shorter than in the regions. Residents of the regions, in order to go to work at a medical or educational institution, have to walk several kilometres in certain cases to reach a stop of the relevant PT route (Figure 5).

From the cartogram of PT passenger flows (Figure 6), it can be seen that due to inaccessibility, residents prefer to use their own cars, so there are many sections of PT routes that do not transport passengers. Long distances between stops cause inconvenience to the passenger, as they increase the walking time [28].

It is clear that the highest passenger flows are generated in the largest elderships: the eldership of Tauragė city, the eldership of Jurbarkas city, and the eldership of Šilalė city. The lowest passenger flows are generated in Juodaičiai eldership, Palentinis eldership, Didkiemis eldership, and Teneniai eldership. The resulting OD matrix shows that the majority of passenger trips are made from city elderships (from 7142 to 26,078 trips/month), and the least amount of passenger trips are carried out from the eldership of Palentinis (130 trips/month). It is evident that the number of passenger trips in larger elderships is higher compared to elderships with a lower population density and number of jobs. PT services are not organized to the elderships of Gaurė, Žygaičiai, Šimkaičiai, Palentinis, and Žadeikiai. Passenger trips to these zones are equal to 0. This is not the case in the city’s OD matrix, since there is a higher demand for PT in cities. It is also easier to estimate passenger transfers in city models.

The Tauragė County model results of passenger loads at stops are shown in Figure 7.

It can be seen from the cartogram that the regions are characterized by a lower density of stops and less load of those stops. There are several stops where the passenger load is high. Compared to PT passenger flows in cities, passenger flows in regions are smaller and uneven.

5.3. Main Suggestions for Creating a PT Demand Model in the Regions

Most of the literature sources describe the specifics that are applied to urban areas. Here, the authors describe the main suggestions for change if the urban area changes to a low-density area. The main suggestions for creating a PT demand model in the regions that consist of low-density areas are:

• In contrast to cities, the distribution of the population in the regions is uneven. In the regions, the population is scattered. In cities, the peak hours model is usually used, as the highest passenger flows are reached during the morning peak hours, when the most important problems become apparent. This is not suitable for region models. Therefore, when modeling PT in the regions, one should choose either a period of one working day or one working week. In more rural areas, PT services are infrequent, end early in the evening, and are not available on weekends. Taking into account the fact that there are regions with PT routes that operate only on certain days of the week (not every day) with limited hours and only once or a few times a day, it is necessary to choose a study period suitable for that region.
• When calculating the parameters of the linear regression analysis of trip generation, demographic (population) and statistical data are used, for example, the working population, the number of students, school children, and pre-school children, the number of jobs, and the capacity of educational institutions, pre-schools, etc. This all depends on what data are available. The number of trip models is selected based on available data. If data are missing, only daily trips can be used, excluding leisure trips.
• Household and roadside surveys are traditional types of surveys, while license plate travel surveys are a new type of survey that is used to determine the OD matrix of cities. The household survey is reliable and accurate, but it requires a lot of time and labor. It is even more difficult to carry out such studies in regions, so determining the OD matrix in regions requires the use of the gravity model, which is no less accurate or precise, by choosing appropriate parameters a, b, c of the combined function. To determine the spatial distribution of trips, research on the transport behavior of residents (including movement relations) according to motivation is needed. If such data are not available, the function parameters a, b, c from other similar regions where such function parameters have been developed can be adopted. This is acceptable for synthetic models.
• The trip assignment stage determines the value of the IPD, which demonstrates what most determines the mode and route of travel. When calculating the IPD for a specific low-density region, it is necessary to estimate the coefficients of PJT indicators based on survey results, explaining why residents do not use PT. It is essential to consider the reasons for PT passenger dissatisfaction. Additionally, conducting a regression analysis and taking into account its results is crucial, e.g., to identify the key indicators influencing PT passenger flows in the region.
• The coefficient of determination, a measure of the difference between the modeled and observed values of the dependent variable, is used to calibrate and validate the PT demand model in the regions. The coefficient of determination is just above the widely used significance threshold of 85%. The higher the value of the coefficient of determination, the better the model fits the data.

6. Conclusions

There is very little in the literature describing demand modeling for low-density areas. A PT service to such areas is vital as it is sometimes the only mode of transport to complete the journey. Addressing the unique challenges of low-density regions in demand modeling is crucial for designing effective transportation systems that cater to the specific needs of these areas. Moreover, understanding the demand patterns and preferences in such areas is essential for optimizing PT services, ensuring their accessibility, and promoting sustainable mobility options.

Traditional surveys (household and roadside) and newer license plate travel surveys determine a city’s OD matrix. While household surveys are reliable, they are time-intensive. A regional OD matrix requires to use of a gravity model, which achieves accurate results by selecting appropriate parameters (a, b, c) for the combined function. Determining the spatial trip distribution requires research on residents’ transport behavior and motivations. In the absence of data, the function parameters from similar regions with established functions can be adopted.

There is no need to worry that many fields are filled with 0 after receiving the results of the OD matrix. This does not mean that there is no need for a PT service in these areas. On the contrary, it indicates that these areas are currently inaccessible to PT services, and residents are confronted with the so-called “last kilometer problem.” This challenge highlights the limited connectivity or proximity of PT stops to certain residential zones, making it difficult for residents to access and benefit from public transportation. Addressing the last kilometer problem is crucial for enhancing the inclusivity and effectiveness of PT networks, ensuring that even areas with currently low or zero demand can become integral parts of a comprehensive and accessible transportation system.

Based on the regression analysis results and the results of the population survey carried out by Green Region, during the trip assignment step, when calculating the IPD, the highest values were assigned to the number of transfers, the walking time to the starting stop, and the walking time to the destination (from the last drop-off stop) coefficients. This emphasizes the significance of these factors in influencing transportation choices and highlights the importance of considering them in the development of effective trip models for the region.

The peak hour model applicable in cities does not apply to regions. The model developed for the region has its own specifics, such as an uneven population density and large differences in the need for PT in terms of place and time. For modeling studies of low-density residential areas, it is best to run the model for five working days, as the timetables and frequency of PT routes in the regions can vary significantly from one working day to another. Of course, the choice of the model assignment time range must also take into account the available data.

In cities, the distance to the nearest PT stop is much shorter than in the regions. Residents of the regions, in order to go to work or to a medical or educational institution, have to walk several kilometers to reach the stop of the relevant PT route in certain cases. From the cartogram of PT passenger flows it can be seen that due to inaccessibility, residents prefer to use their own cars, so there are many sections of PT routes that do not transport passengers.

When verifying the output of cities’ PT models, the verification process is usually achieved using the GEH statistic. When developing a regional demand model, the model’s validity is assessed through the use of the coefficient of determination. The calibration of the region model’s coefficient of determination obtained from the analysis of the double-squared dependency is above the widely used significance threshold of 85% and is equal to 86.7%. This means that the model is reliable and reflects the current situation, so the developed Tauragė County PT model can be used for further research, experimentation, and the development of a methodology for organizing PT in the region.

It is important to note that the specifics presented for developing demand modeling can be applied to any low-density region. Recognizing the universality of these specifics and presenting main suggestions allows for a more widespread and adaptable approach to addressing the unique challenges encountered in low-density areas. Of course, the specifics can be revised, taking into account the region’s existing culture, faith, and travel patterns.